Is there someone out there with any experience with the two lenses?
Based on this comparison from The-Digital-Picture there is a slight gain in sharpness with the new lens. Probably not enough difference to be noticed in real world comparisons between images printed at typical sizes and viewed at typical distances. Keep in mind the differences are small enough they could be attributed to copy-to-copy variation between two lenses with almost identical optics. The review specifically mentions one lens is sharper in the top left corner, the other is sharper in the lower right corner:
If I want to make the STM look better, I don't show the bottom right. And vice versa. My 18-135mm IS STM Lens delivers a better image on average, but it is not better enough to land it in a higher class than my pervious version 18-135mm IS Lens.
The primary difference is the focus performance for shooting video, both in terms of focus accuracy while recording and less noise produced by the focus motor that can be picked up in the recording.
If you've already got the EF-S 18-135mm f/3.5-5.6 IS it is probably not worth the price of the upgrade, especially if all you do is shoot stills. If you shoot video with the in camera microphone as your audio source it might then be worth it.